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All the latest psychoanalytic theory has been pursuing a highly mathematized trajectory which has left me in the dust as a philosophy/psychology student (4 years of liberal arts college with no math or science prerequisites).

What sort of math curriculum would one need to undertake to "keep up with the Joneses"? The Joneses being the French nonphilosophers and psychoanalysts.

Can anyone recommend any books for learning said curriculum?

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    I feel like I'm always hawking this text, but Zalamea's Synthetic Philosophy of Contemporary Mathematics is fantastic – Joseph Weissman Apr 25 '14 at 0:08
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    I found this ... lacanianworks.net/?p=126. The use of topology by Lacan appears to be entirely metaphorical. No math knowledge whatever is required. You just have to find some pictures of Moebius strips, Klein bottles, and the like; and then let your mind drift away in a postmodernist haze. That's my take from the article, anyway. Am I missing something? – user4894 Apr 25 '14 at 1:26
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    As a math student who knows very little about Lacan, the brief reads I made doesn't have any mathematics at all and is just pure gibberish nonsense (mathematically speaking), if it isn't methaphorical, I'd say it isn't nothing at all. This is a point highly critized about Lacan, I recommmend you the read the first chapter of the book "Fashionable Nonsense" which is about Lacan and mathematics. – Gabriel Apr 25 '14 at 2:12
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    Agreed with Dante. I would add Feynman's explanation of the reasons why social scientists sometimes make nonsensiccal references to Math and Science. – Michael Apr 25 '14 at 6:33
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    what kind of terms are being discussed? My impression its mainly logic, topology & knots - The (very small) book knots by Sossinky is brilliant about why knots matter to mathematicians; and as it is directed towards the layman - it doesn't contain any serious mathematics in the sense serious is understood in mathematics, ie proofs & exercises. – Mozibur Ullah Apr 25 '14 at 13:33
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I read this guy's Part II where he fits together the 4 formulae, the 4 discourses and topology as Lacan puts it forth in L'etourdit. The argument is that in no way is Lacan's use of topology metaphorical.

http://www.academia.edu/5984726/Sexuated_Topology_and_the_Suspension_of_Meaning_A_Non-Hermeneutical_Phenomenological_Approach_to_Textual_Analysis

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I do not know what "Lacanian topology" is, but for knot theory, the prerequisite is a basic course in algebraic topology.

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This isn't an answer per se to your question; but as a cautionary tale against dismissing mathematical formalism in unexpected locations in the human sciences. Its also much too long to go into a comment.

Jack Morava, a distinguished mathematician published this paper 'On the Canonical formula of C. Levi-Strauss', he writes in the abstract:

The anthropologist Claude LeviStrauss has formulated a theory of the structure of myths using a formalism borrowed from mathematics, which has been difficult to interpret, and is somewhat controversial. Nevertheless, LeviStrauss's old school chum Andre Weil took his work seriously, and in this note I propose an interpretation of LeviStrauss's `canonical formula' in terms of an anti-automorphism of the quaternion group of order eight.

The canonical formula is discussed in detail and in practise in a volume of essays of ethnography by Maranda, The Double Twist; this includes an essay by Levi-Strauss on 'Hour-glass configurations' on Melanesian cosmography (Yeats gyre comes to mind here).

looks cryptic to most scholars - mathematicians, social scientists and humanists alike. it reads: f_x(a):f_y(b)::f_x(b):f_(a^-1)(y)

Morava adds in the conclusion:

I hope those who read this will not be offended if I close with a personal remark. When I first encountered L´evi-Strauss’s formula, my reaction was bemusement and skepticism; I took the question seriously, in large part because I was concerned that it might represent an aspect of some kind of anthropological cargo-cult, based on a fetishization of mathematical formalism. I am an outsider to the field, and can make judgements of L´evi-Strauss’s arguments only on the basis of internal consistency, (in so far as I am competent to understand them); but I have to say that I am now convinced that the man knows his business.

Structural anthropology by Levi-Strauss was of course a key entry point into (structuralism in the Humanities); and Strauss's matheme (which is always a token, but possibly also a sign in the written discourse of mathematics, and is as phoneme is to the spoken discourse of some language in linguistics) is seen to be strict, that is stenographic in Moravas analysis.

A second surprising application of topology is in mathematics itself. Actual formulas in category theory (ie written out in a sequence of symbols) can be translated into a string or knot or tangle diagram; these can be manipulated as one would do as a topological object - and the final configuration when translated back into symbols remains valid.

This of course has been doe before, principally through Descarte - an algebraic formula is equivalent to a geometric one. But of course here the geometry is rigid, and not floppy as in topology.

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